Taxes, wages and working hours

Abstract

This paper presents estimates of individuals’ responses in hourly wages to changes in marginal tax rates. Estimates based on register panel data of Swedish households covering the period 1992 to 2011 produce significant but relatively small net-of-tax rate elasticities. The results vary with family type, with the largest elasticities obtained for single males and the smallest for married/cohabitant females. Despite these seemingly small elasticities, evaluation of the effects of a reduced state tax using a microsimulation model shows that the effort effect matters. The largest effect is due to changes in number of working hours yet including the effort effect results in an almost self-financed reform. As a reference to the earlier literature, we also estimate taxable income elasticities. As expected, these are larger than for the hourly wage rates. However, both specifications produce significantly and positive income effects. One contribution is related to the definition of the instruments used to solve the well-known problem of endogeneity.

Appendices

Appendix 1: Replicating the wage elasticities in Blomquist and Selin

As mentioned above, our estimates deviate from the ones presented in Blomquist and Selin, especially for the females—strong incentive effects in Blomquist and Selin compared to essentially zero effects in our study. The main differences between our paper and Blomquist and Selin are the covered time period, the size of the sample as well as the choice of instruments. In order to make our results as comparable as possible, we include two time periods, 2000 and 2011, and use the same method for selecting instruments. However, there still remains important differences—different time period, sample size and source of information used for defining hourly wages.

Blomquist and Selin derive the following statistical model, including parameters $\gamma _{0}, \gamma _{1}, \gamma _{2}$ and $\gamma _{3}$.

$$\begin{aligned} \ln \left( {\frac{{W}_{{i}1991}}{{W}_{{i}1981} }} \right) \!=\!\gamma _0 \!+\! \gamma _1 \ln \left( {\frac{1-\tau _{{ i}1991}}{1\!-\!\tau _{{i}1981}}} \right) +\gamma _2 \ln \left( {\frac{{M}_{{i}1991}}{M_{{i}1981}}} \right) +\gamma _{3} {X}_{{i}1981} + {f}(\hbox {ln} {\overline{\hbox {TLI}_{i}}})+(\varepsilon _{{i}1991} -\varepsilon _{{i}1981}) \end{aligned}$$

The parameters $\gamma _{1}$ and $\gamma _{2}$ correspond to the wage elasticity with respect to net-of-tax and virtual income.

Our estimates of this model produce elasticities approximately similar to our earlier results. However, our estimates for females are much lower than the results in Blomquist and Selin. There are many possible explanation of this discrepancy—important one is that our time period does not include the major tax reform 1991.

See Table 8.

Table 8 A comparison of wage elasticities

Appendix 2: A Swedish behavioral microsimulation model SWEtaxben

The tax/benefit part of SWEtaxben is primarily a tool to calculate the households’ budget set. For the two-earner household, the budget (disposable income or net income after tax and transfers) evaluated at observed working hours is given as

$$\begin{aligned} {C}&= {I}_{{m}}+{I}_{{f}} + {B}_{\mathrm{s}}+{B}_{\mathrm{h}}-{B}_{\mathrm{c}} \quad \hbox {where}\, {I}_{{i}}\nonumber \\&= {W}_{{i}} {H}_{{i}}+{Y}_{{i}}+{V}_{{i}}-{t}({X}_{{i}}), {i}={m} (\hbox {male}), {f} (\hbox {female}) \end{aligned}$$

(2)

Apart from hourly wages, ${W}_{{i}}$, and yearly number of working hours, ${H}_{{i}}, {Y}_{{i}}$ represents non-earned taxable income (e.g., capital income, old-age pension and benefits from unemployment, disability and long-term sickness) and ${V}_{{i}}$ non-earned non-taxable income (e.g., child allowance); t is a tax function defined on taxable income, ${X}_{{i}}, ({X}_{{i}}= {W}_{{i}}{H}_{{i}}+{Y}_{{i}}-{D}_{{i}}$ where ${D}_{{i}}$ is deductions for work-related expenses or part of the premium for private pension savings). The three mean-tested (i.e., dependent on ${H}_{{i}}$) transfers considered are social assistance (${B}_{\mathrm{s}}$), housing allowance (${B}_{\mathrm{h}}$) and cost of child care (${B}_{\mathrm{c}}$). It is a considerable advantage that these systems are based on nationwide rules.

In order to understand the sequential steps involved in the simulation, it is instructive to start by dividing the sample into the following subgroups:

(1) Child, age 0–15, (2) Old-age pensioner, age 61-, (3) Student, (4) Disability pensioner, age 18–64, and old-age pensioner after 64, (5) Parental leave, (6) Unemployed, age 18–64 and old-age pensioner after 64, (7) Other (no income from states 2–6, 8, 9 but can have income from social assistance), (8) Long-term sick, age 18–64, and old-age pensioner after 64 and (9) Working, age 18–70, and old-age pensioner after 70.

This classification refers to a full-time status during the base year (2007) and is primarily based on the main source of income. Individuals who got their main income from old-age pension are classified as pensioners, and so on. There are also some age-related criteria that overrule the income source. Thus, all individuals younger than 16 are classified as child, and all individuals above 70 as old-age pensioner. An individual can only be classified as disabled, unemployed or long-term sick up to age 64; above this age, he is classified as an old-age pensioner. The main reasons for splitting the population into these categories are that these categories represent different subsamples that are relevant from a policy perspective. What effect does an economic reform has on old-age pensioners, unemployed working and so on? Most of these categories correspond to stochastic models that decide the in- and outflow.

The main sequential steps are given in Fig. 6. The first step (see Fig. 6) involves the definition of a replacement rate for disability pension. The population at risk (that is the individuals who are exposed to the stochastic model) comprises individuals age 18–64 (but not older children living together with their parents) with a status of disabled/unemployed, long-term sick or working. For couples, at least one of the spouses has to belong to the population at risk. For each individual in this population, the tax/benefit module is called upon to calculate disposable income assuming that everyone is classified as being on full-time disability. Next, for the same individuals, income is calculated assuming full-time work ($H=1{,}800$). The ratio of disposable income from disability divided by disposable income from work defines the replacement rate. For instance, a replacement rate of 0.7 means that an individual who receives full-time compensation from disability insurance receives 70 % of the disposable income he would have received had he been a full-time worker. A change in a tax/benefit that has an effect on the replacement rate will also have an effect on the probability of entering, staying in, or exiting from disability.

Fig. 6

Structure of SWEtaxben

Given the replacement rate, as well as all other explanatory variables included in the model, the probability of disability is calculated. In the calculation of this probability, two stochastic terms enter: first a random draw from a normal distribution (with an estimated mean and variance) representing individual heterogeneity and second a Monte Carlo experiment. If the simulated probability is less than a random draw from a uniform (0–1) distribution, then the event takes place; that is, the individual is classified as disabled. Individuals not classified as disabled get the temporary status (10) and enter the next stochastic model in the sequence. Note that the random errors for each individual are the same before and after a reform. The Monte Carlo experiment acknowledges the fact that even individuals whose characteristics are such that the likelihood of disability are very low still face the risk of “bad luck.” With appropriate changes, the same argument also applies to an individual with a high systematic probability of disability. This stochastic experiment has been applied to all binary events in the model.

The next step involves unemployment, and the population at risk is unemployed, long-term sick or working and those with the temporary status. The steps undertaken are the same as for disability. Thus, after this step, the individuals in the risk population are classified either as unemployed or as being in the temporary state. However, an important difference is that a submodel is used to classify individuals as half- or full-time unemployed. After this follows the simulation of the individuals classified as long-term sick, the population at risk is individuals classified as long-term sick or working and those with the temporary status. Again, the same procedure is used, and as a result of this module, individuals now belong to the status long-term sick or temporary. The final binary model concerns old-age pension; the population at risk is old-age pensioners, other or working and those with temporary status age 61–70. An individual younger than 61 is not eligible for old-age pension, and all individuals above the age of 70 are by default old-age pensioners. Again after this step, individuals are classified as old-age pensioners or are in the temporary state.

After these binary models, a simple imputation follows, where all individuals with the temporary status who before the reform belonged to one of the binary states, i.e., individuals who have exited one of the binary states without entering another, are imputed as entering the working state and are given a number of yearly working hours equaling 1,800.¹¹ This concludes the first part of the model where the binary models are used. Next, we will explain the imputation of working hours and social assistance.

Every individual in the risk population (status other or working) is considered as working or voluntarily non-working. Thus, this is the typical risk population in traditional labor supply studies. For every individual in this population, the tax/benefit module is called upon repeatedly in order to evaluate the budget set. For individuals classified as singles, this requires 14 calls (7 working classes with and without social assistance), and for couples, the creation of the budget set requires 98 calls $(7\times 7\times 2)$.¹² Note that for the couples, at least one of the spouses should belong to the population at risk. Given the budget set and all other variables included in the labor supply models, working hours as well as the probability of social assistance are predicted. The stochastic experiment for those models involves draws from an extreme value distribution. Also, note that different models have been estimated depending on the family type.

At this stage of the simulation, every individual has a predicted status, predicted working hours and predicted welfare participation. After this, the next step in the simulation is to use the estimated elasticities from the wage equation in order to simulate the wage responses. The population at risk comprises all individuals with positive hours of work before and after the reform. Of course, this separate treatment of hours and wages represent a simplification. For instance, higher hourly wage rates can be related to higher annual hours of work, and indeed, Fig. 5 also suggested such a pattern, at least for females.

A final step is to call the tax/benefit module again to get the predicted disposable income, calculated at the predicted values of working hours, social assistance and wages. Thus, this is the predicted disposable income for the individuals/households resulting from the tax/benefit rules. By changing these rules and repeating the simulation, disposable income before and after a reform can be compared.

Obviously, the results of the simulations are dependent on the econometric models, and as mentioned above, four econometric models are used to simulate the probability of disability, unemployment, long-term sickness and old-age pension, and for the conditional labor supply different discrete choice models have been estimated for each family type. All of the binary models have been estimated as dynamic random-effects logit models. The data used for the estimation is a balanced LINDA panel from 2000 to 2006. The method used for the conditional labor supply models follows previous work by Van Soest (1995); the household model is described in Flood et al. (2004) and the model for the single-headed household in Flood et al. (2007). These models belong to the class of discrete choice model, and an advantage of this approach is that it allows us to include as many details regarding the budget set as needed and that it extends naturally into a household model, where husbands and wives jointly determine their labor supply.¹³